Neural network study of the nuclear ground-state spin distribution within a random interaction ensemble

The distribution of the nuclear ground-state spin in a two-body random ensemble(TBRE)was studied using a general classification neural network(NN)model with two-body interaction matrix elements as input features and the corresponding ground-state spins as labels or output predictions.The quantum many-body system problem exceeds the capability of our optimized NNs in terms of accurately predicting the ground-state spin of each sample within the TBRE.However,our NN model effectively captured the statistical properties of the ground-state spin because it learned the empirical regularity of the ground-state spin distribution in TBRE,as discovered by physicists.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

Structure and analytical potential energy function for the ground state of the BC^x （x=0, -1）

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.

Ground states for asymptotically periodic quasilinear Schrdinger equations with critical growth

For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.

A Comparative Study of Fractional Order Models on State of Charge Estimation for Lithium Ion Batteries

State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have provided a distinct insight into SOC estimation.In this article,we compare five state-of-the-art FOMs in terms of SOC estimation.To this end,firstly,characterisation tests on lithium ion batteries are conducted,and the experimental results are used to identify FOM parameters.Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy.The model R(RQ)W shows superior identification accuracy than the other four FOMs.Secondly,the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles,memory lengths,ambient temperatures,cells and voltage/current drifts.The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs.Although more complex models can have better robustness against temperature variation,R(RQ),the simplest FOM,can overall provide satisfactory accuracy.Validation results on different cells demonstrate the generalisation ability of FOMs,and R(RQ)outperforms other models.Moreover,R(RQ)shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.

Theoretical Study of Geometric Structures for Ground-state Al_nC(n=2-7) Clusters

With the aid of the molecular orbital DMol3 program,the energetics and electronic structures of several AlnC（n = 2-7） configurations have been searched and calculated by improved minimum energy paths（MEPs） by setting ＂imaging product＂.A new high symmetry,supervalence isomer of Al5C cluster,i.e.,D5h-Al5C,at the local minimum in the MEPs is detected.Several parameters,such as binding energy,HOMO-LUMO energy gap,vertical electron detachment energy and electron affinity energy,are calculated to characterize and evaluate the stability of three Al5C configurations,i.e.,D5h-Al5C,Cs-Al5C and C1-Al5C.The results show that the D5h-Al5C cluster is the ground state structure instead of Cs-Al5C.Due to the formation of many central σ bonds after polymerizing for D5h-Al5C,the decrease of the energy for HOMO orbit results in more territory for HOMO electrons of dislocation effect,then the energy difference between HOMO and LUMO is increasing to enhance the stability of molecules to produce such supervalence structure of Al5C cluster.The configuration evolution between D5h-Al5C,Cs-Al5C and C1-Al5C and the synthesis preference in the mode of Al5 ＋ C → Al5C reveals that the Cs-Al5C and C1-Al5C con-figurations are permissive to coexist with D5h-Al5C structure in energetics.

Ground-State Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal-Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,

GROUND STATE SOLUTIONS FOR THE CRITICAL KLEIN-GORDON-MAXWELL SYSTEM

In this article,we study the following Klein-Gordon-Maxwell system involving critical exponent■where λ and w are two positive constants.We found the existence of positive ground state solutions(that is,for solutions which minimizes the action functional among all the solutions)of(KGM) which improves some previous existence result in Carriao et al.(2012) [8].

GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR A FR ACTIONAL SCHRODINGER-POISSON SYSTEM WITH CRITICAL GROWTH

We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.

GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equations qn=U＇（qn＋1-qu）-U＇（qn-qn-1）,n∈Z,where qn denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth （Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 （2009）, 3802- 3822）, we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.

ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.

Extended state observer-based control with an adjustable parameter for a large ground-based telescope

The high-precision requirements will always be constrained due to the complicated operating conditions of the ground-based telescope. Owing to various internal and external disturbances, it is necessary to study a control method, which should have a good ability on disturbance rejection and a good adaptability on system parameter variation. The traditional proportional-integral(PI) controller has the advantage of simple and easy adjustment, but it cannot deal with the disturbances well in different situations. This paper proposes a simplified active disturbance rejection control law, whose debugging is as simple as the PI controller, and with better disturbance rejection ability and parameter adaptability. It adopts a simplified second-order extended state observer(ESO) with an adjustable parameter to accommodate the significant variation of the inertia during the different design stages of the telescope. The gain parameter of the ESO can be adjusted online with a recursive least square estimating method once the system parameter has changed significantly. Thus, the ESO can estimate the total disturbances timely and the controller will compensate them accordingly. With the adjustable parameter of the ESO, the controller can always achieve better performance in different applications of the telescope. The simulation and experimental verification of the control law was conducted on a 1.2-meter ground based telescope. The results verify the necessity of adjusting the parameter of the ESO, and demonstrate better disturbance rejection ability in a large range of speed variations during the design stages of the telescope.

Rotational Population Measurement of Ultracold 85Rb^133Cs Molecules in the Lowest Vibrational Ground State

We measure the rotational populations of ultracold SS Rbla3 Cs molecules in the lowest vibrational ground state by a depletion spectroscopy and quantify the molecular production rate based on the measurement of single ion signal area. The SSRb133Cs molecules in the X1∑＋（v = 0） are formed from the short-range （2）^3П0＋（V = 10, J = 0） molecular state. A home-made external-cavity diode laser is used as the depletion laser to measure the rotational populations of the formed molecules. Based on the determination of single ion signal, the production rates of molecules in the J=0 and J = 2 rotational levels are derived to be 4800mole/s and 7200mole/s, respectively. The resolution and quantification of molecules in rotational states are facilitative for the manipulation of rotational quantum state of ultracold molecules.

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SOLUTIONS FOR CHERN-SIMONS-SCHR?DINGER SYSTEMS WITH A STEEP WELL POTENTIAL

In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.

GROUND STATE SOLUTIONS FOR A SCHRODINGER-POISSON SYSTEM WITH UNCONV ENTIONAL POTENTIAL

We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of nonnegative ground state solutions is established.Our method relies upon the variational method and some analysis tricks.

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.

EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.

Asymptotical consensus of fractional-order multi-agent systems with current and delay states

In this paper,we study some new fractional-order multi-agent systems with current and delay states (FMASCD).Using the generalized Nyquist's stability criterion and Gerschgorin's circle theorem,we obtain the bounded input-bounded output (BIBO) stability and asymptotical consensus of the FMASCD under mild conditions.Moreover,we give some numerical examples to illustrate our main results.